A353615 a(n) is the numerator of the median abundancy index of the first 2^n + 1 positive integers.

4, 4, 13, 3, 32, 45, 63, 90, 111, 162, 210, 237, 7502, 11776, 240, 2944, 3008, 11648, 225152, 478080, 2704000, 1548160, 2462400, 10128256, 4999296, 8640768, 48264064, 32347648

Offset

1,1

Comments

The abundancy index of a number k is sigma(k)/k = A017665(k)/A017666(k), where sigma is the sum-of-divisors function (A000203).

Links

Table of n, a(n) for n=1..28.

Formula

Limit_{n->oo} a(n)/A353616(n) = A353617.

Example

The fractions begin with 4/3, 4/3, 13/9, 3/2, 32/21, 45/29, 63/41, 90/59, 111/73, 162/107, ...
The abundancy indices of the first 3 positive integers are 1, 3/2 and 4/3. The median is a(1)/A353616(1) = 4/3.

Mathematica

With[{m = 20}, t = Table[DivisorSigma[-1, n], {n, 1, 2^m + 1}]; Numerator @ Table[Median[t[[1 ;; 2^n + 1]]], {n, 1, m}]]

Crossrefs

Cf. A000203, A017665, A017666, A353616 (denominators), A353617.

Sequence in context: A228612 A038804 A183362 * A088838 A367688 A127403

Adjacent sequences: A353612 A353613 A353614 * A353616 A353617 A353618

Keyword

nonn,frac,more

Author

Amiram Eldar, Apr 30 2022

Status

approved